The rate of oxygenation for a stream from atmospheric reaeration depends on many

Question

The rate of oxygenation for a stream from atmospheric reaeration depends on many physical parameters^3. A simple, but useful, engineering model proposed by Thayer and Krutchkoff^4 in 1966, relates the rate of oxygenation with the mean velocity, V [fps], and average depth, H [ft], of the stream flow. E(X|V, H) = alpha V^beta _1 H^beta _2 (5) Using the data given in the Table 2 estimate the model coefficients alpha, beta _1 and beta _2, and evaluate the corresponding conditional standard deviation. Clearly and unambiguously state the least squares model that you are fitting^5.

Explanation / Answer

E[ X/V,H] = V1H2

By taking logarithm of given equation

ln [E] = ln + 1ln V+ 2ln H

Now we will do multiple linear regression. I have done it in excel.

The below is logarithm table

Blow given is regression analysis table:

so now putting value in the linear equation

ln [E/X] = ln + 1ln V+ 2ln H

so here ln = 1.5164

= 4.555 ; std. dev. = 0.6362

1= 0.879 ; std. dev. = 0.4770

2= - 1.50 ; std. dev. = 0.2070

The model logarithmic linear regression.

V[fps] H(ft) X(ppm/day) ln V ln H ln X 3.07 3.27 2.272 1.121678 1.18479 0.820661 3.69 5.09 1.44 1.305626 1.627278 0.364643 2.1 4.42 0.981 0.741937 1.48614 -0.01918 2.68 6.14 0.496 0.985817 1.814825 -0.70118 2.78 5.66 0.743 1.022451 1.733424 -0.29706 2.64 7.17 1.129 0.970779 1.969906 0.121332 2.92 11.41 0.281 1.071584 2.43449 -1.2694 2.47 2.12 3.361 0.904218 0.751416 1.212239 3.44 2.93 2.794 1.235471 1.075002 1.027474 4.65 4.54 1.568 1.536867 1.512927 0.449801 2.94 9.5 0.455 1.07841 2.251292 -0.78746 2.51 6.29 0.389 0.920283 1.838961 -0.94418

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.